Data-driven Synchronization for Network Systems with Noiseless Data

TL;DR

This paper develops a data-driven method to achieve synchronization in homogeneous networked LTI systems without requiring explicit system models, using only input-state data from a single system.

Contribution

It provides necessary and sufficient data-based conditions for network synchronizability and a direct data-driven feedback gain design method.

Findings

Conditions for network synchronizability derived from data

Explicit feedback gain can be obtained from data

Numerical simulation validates the approach

Abstract

For a collection of homogeneous LTI systems that is interconnected by a protocol, given the network topology and the system model, one may obtain a feedback gain to synchronize the network. However, the model-based methods cannot be applied in case the system model is unknown. Therefore, in this paper, we study the data-driven synchronization problem for homogeneous networks. In particular, given a collection of LTI systems, we collect the input-state data from one individual system. Then, given the network topology, we provide data-based necessary and sufficient conditions for synchronizability. Once the conditions are satisfied, one can also obtain a feedback gain directly from data to synchronize the network with the corresponding design method provided in this paper. Finally, we illustrate our results with a numerical simulation.